After my book appeared, legions of blackjack players hit the tables in Nevada. Anyone could bring the book’s palm-sized strategy cards and find a game with rules good enough to let them play on level terms with the casino, even without counting cards. Then there were the card counters and would-be card counters. Many were good and some would go on to make their living from blackjack, but for the majority the effort and persistence required to practice card counting, the restraint and discipline needed, to say nothing of the temperament, were obstacles to success.
Still, the fact that blackjack could be beaten led to an upsurge in play. As a result, during the next few decades blackjack displaced craps as the dominant table game. However, the casinos were in a bind: Should they let the minority of players who were counters beat them in return for the vastly increased revenues from the great majority of players who couldn’t or wouldn’t count, or should they try to choke off the card counters with countermeasures, even if this would slow the boom in blackjack play?
When the casinos first tried a rules change and lost more in revenues than they gained in benefits, they went back to the old rules. Next, they brought in dealing boxes known as shoes, which allowed the use of four, six, or even eight decks. This was supposed to make card counting more difficult. But for those who used the High–Low System, it wasn’t much harder. That was because the correct play of the hand was pretty much the same for various numbers of decks and because the High–Low System already adjusted for the number of unused cards, whether the game was played with one or several decks. The good players, who were getting better with practice, continued to win.
The most widely used photo gallery of undesirables was developed for the casinos by Griffin Investigations, Inc., a private detective agency founded in 1967 by Beverly and Robert Griffin. The usual collection of criminals, player cheats, and public nuisances was rapidly expanded by the addition of ever more card counters. They were barred on sight, and their descriptions were shared among the casinos. However, dealers and pit bosses often couldn’t figure out who was counting and who wasn’t. Non-counters who inadvertently aroused suspicion were, to their bafflement, forbidden to play. Players were cheated and beaten in back rooms. Eventually the Griffin agency was successfully sued by two top card counters, one of whom was James Grosjean, a member of the Blackjack Hall of Fame, and the firm filed for bankruptcy in 2005.
Card counters formed informal networks and developed new and improved techniques. Beat the Dealer had introduced the idea of a team. Suppose several players, say five, each with a $10,000 bankroll, are playing separately, winning at an average rate of 1 percent or $100 an hour. Then the five players together will gain an average of $500 an hour. If instead they pool their money into one $50,000 bank, when one of them plays he can bet five times as much as he could safely risk on his own $10,000. Consequently he expects to win five times as much, namely, 1 percent of $50,000 or $500 per hour, rather than $100. But it gets better. The four other players can all be playing, too, typically at different tables or casinos, acting as though they each have a $50,000 bankroll, so the group makes $2,500 per hour when all are playing whereas, playing without pooling their bankrolls, they would make collectively only $500 an hour.
The next step was obvious. Entrepreneurs went into the blackjack business by recruiting and training players, providing a bankroll, and sharing the profits between the players and the financier. Notable teams include Tommy Hyland’s and the now famous MIT group, chronicled in the book Bringing Down the House, which inspired the 2008 movie 21. Al Francesco pioneered the creation of blackjack teams, and the idea was well publicized by one of his recruits, Ken Uston (1935–87). Uston’s books Million Dollar Blackjack and The Big Player inspired the formation of other teams as well as intensifying casino efforts to stop them. Ken Uston was one of the more colorful characters in blackjack history. One-quarter Asian, with a Japanese grandfather, he was born Kenneth Senzo Usui. Starting his career in the securities business, he became the youngest senior vice president ever at the Pacific Stock Exchange. Drawn by the allure of blackjack he then left the securities industry to play professionally.
Card counters wish to bet as little as possible when the casino has the edge, then make a large bet when the cards favor them. Ideally, a player with a bankroll large enough to allow $1,000 bets when the deck is favorable would bet the table minimum, say $5, when it isn’t. Such a wide betting spread of 200:1 is a red flag to casino personnel. But to bet $1,000 on good situations with a narrower betting spread of, say, 4:1 requires $250 bets when the deck is unfavorable. This cuts back the overall gain.
The remedy was to use what was called a Big Player. Teams placed members at several blackjack tables to track the deck, meanwhile betting the minimum. When a deck became favorable they signaled the Big Player, who seemed to wander randomly from table to table, putting down sizable bets erratically. Since he hadn’t been at the table before he bet, he couldn’t be counting. All this was disguised with an act. The Big Player might appear to be a drunken flamboyant high-roller, often with a beautiful companion.
Meanwhile, the blackjack community was exploring and developing the various possible counting methods. These followed directly from my original computations showing the effects of removing various cards from the deck. A counting system assigns points to each card that reflect the card’s impact upon removal. The closer these points correspond to the actual effects of the cards, the more accurately that particular counting method estimates the player’s current edge.
To illustrate this basic idea I presented what I called the ultimate strategy, which assigned a whole number value to each card in close proportion to its impact on the odds. The numbers in table 1 are from the 1962 edition of Beat the Dealer. The second line shows the change in the player’s edge upon removing one card. The third line, obtained by multiplying by 13 and rounding to the nearest whole number, gives the point count for the ultimate strategy, a good approximation to a perfect point count. Because of the diverse point values, I expected this system to be used by computers, not people. I intended it only to illustrate the basic principle for constructing point-count systems—the closer the point assignments were to the effects of the corresponding cards, the more powerful the system. On the other hand, the more diverse the point values used for a particular card counting system, the harder that count was to use.
Card |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
A |
Change In Edge |
0.36 |
0.48 |
0.59 |
0.82 |
0.47 |
0.34 |
0.03 |
-0.23 |
-0.54 |
-0.68 |
Points |
5 |
6 |
8 |
11 |
6 |
4 |
0 |
-3 |
-7 |
-9 |
Perhaps the best compromise between power and simplicity is the High–Low, or the Complete Point Count, which appears in the 1966 revised edition of Beat the Dealer. Still used today by top professionals, this is the simplest possible point count in that cards get values of −1, 0, or +1 only. You start with the count at 0. As the “small” cards 2, 3, 4, 5, 6 are used, they each add +1 to the cumulative count. The intermediate cards 7, 8, and 9 are counted as 0 so their appearance doesn’t affect the total count. Big cards—Aces and Ten-value cards—count as −1 so they each reduce the total by one.
Suppose the player using the High–Low count sees these cards in the first round of play: A, 5, 6, 9, 2, 3. Then the count, which started with zero, becomes −1 + 1 + 1 + 0 + 1 + 1 = +3. With this count in a one-deck game—and with reasonably favorable rules—the player has an edge on the next deal. As cards are dealt, the count goes up and down around zero. When the count is positive the player benefits, and when it is negative it helps the casino. The impact of any particular value of the count is greater when fewer cards are left. Good players simply estimate this by seeing how many cards are in the discard tray.
How hard is it to keep the point count? A typical test is to shuffle the deck, remove one to three cards facedown, then count through the rest of the deck. The player declares the result, then the missing card or cards are turned over to see if he is right. For example, suppose after one card has been set aside without its face being shown, the count for the rest of the deck is zero. Then, since the total count must come out to zero (as you may have already noticed, the complete point count has 20 negative points and 20 positive points in each fifty-two-card deck), the unseen card must be a 0-point card, namely, a 7, 8, or 9. This can lead to some surprises.
One night I was playing in Puerto Rico with the comedian and TV personality Henry Morgan, who was well known in the 1950s and ’60s. I had been losing for an hour or so. At the end of a two-deck shoe, my dealer had a Ten up. As the casino betting limit was $50 per hand, I could get more money on the table and keep out other players by betting on all seven spots. I was using the variation of the point count where the cards 2, 3, 4, 5, 6, 7 are +1, 8 is 0, and 9, 10, A are −1, as they appear. The cards had run out on the deal, and the point count was zero. Therefore the one unseen card, which was the dealer’s hole card, had to be a 0. So the dealer had an 8 in the hole for a total of 18. The deck was reshuffled so I could finish playing my seven hands. Since I had several hands of hard 17 that I alone knew were to be sure losers if I did nothing, I hit them. This is a disastrous choice unless you know the dealer’s hole card, and that he has you beat. Unlucky, I busted every one of them.
The dealer looked up scornfully, saying to me with a laugh, “So you count the cards, amigo. Why, I’ll bet you even know what I’ve got.” As the other dealers grinned, I said, “Why, you have an 8 under there.” The dealer laughingly summoned several other dealers and the pit boss. He explained contemptuously that the Americano expert said that he had an 8 in the hole. A babble of uncomplimentary remarks in Spanish passed back and forth.
I was tired and ready for a break. I had made an occasional counting error over the last hour. There was a chance I would be wrong (better for me if I was, probably). Then the dealer turned over his hole card. It was an 8. The torrent in Spanish raged anew.
How hard is it to count? The more I practiced, the better my times, and I found that if I was able to count one deck in twenty to twenty-five seconds I could easily keep up in any game I was in, so I simply checked to be sure I was up to this standard each time before I played. One of the members of the Blackjack Hall of Fame impressed the professionals by counting two decks in thirty-three seconds. But the most amazing performance I have seen was at the third World Game Protection Conference at the Paris Hotel in Las Vegas. A highlight of one evening’s entertainment was a card counting contest. The choice of technique for handling the cards was crucial for attaining really low times. The winner, among scores of contestants from the casino industry, had the fastest time I ever saw, 8.8 seconds.
The casinos introduced technology to stop the counters. Cameras and observers followed the action through one-way mirrors above the tables. Currently, this is automated, incorporating face-recognition software. RFID chips keep track of a player’s bets, and machines can track the cards and check the play of the hands, searching for patterns characteristic of counters. Machines that continually reshuffle the cards proved to be a perfect defense without slowing the game down, but the casinos pay fees to the vendors of the machines.
Meanwhile the card counters were developing more techniques for winning. One of these methods was based on the fact that the players are dealt two cards each and the dealer also typically receives two cards, the first faceup and the second facedown and hidden under the first. If the dealer’s top card is an Ace or Ten-value card (K, Q, J, 10) then the dealer checks his hidden card to see if he has a natural, or a blackjack, in which case he shows it and all bets are settled at once. A dealer blackjack beats all player hands except another blackjack. A dealer making this hole-card check would typically bend up the corner of his two cards to see what was hidden underneath. Eventually the Aces and Tens would get slightly warped. If the dealer was especially careless or if decks weren’t changed often enough, the savvy player could spot the warps before they were dealt and know where the Aces and Tens were, a huge advantage.
Mining the same ore were the so-called spooks, confederates strategically placed to see the hole-card of a dealer who was careless in checking it. If the dealer does not have blackjack, the play of the hands continues and a player whose spook tells him the value of the dealer’s hidden card gets a huge edge. Some casinos prevent players from using spooks and warps by having the dealer wait to draw his second card until after all the players finish playing their hands. Then the dealer’s second card can be dealt faceup.
In the 1970s, several people developed concealed computers to play blackjack. The casino industry’s response was to have the Nevada legislature pass a law in 1985 outlawing devices that assisted players in calculating odds. But the ingenious players weren’t done yet. When one deck of cards or a multideck pack of cards is shuffled, the shuffling may not be thorough enough to randomize the deck. A deck that isn’t well shuffled may have predictable patterns that can be exploited.
This was a natural evolution from my early thoughts about non-random shuffling back in 1961 and 1962. I realized that the type of shuffle that was used could substantially affect the odds of many games. I designed a two-pronged attack: I would build mathematical models to approximate real shuffling, and do empirical studies of real shuffling.
As a first simple approach for exploiting this, I came up with a way to locate the Aces in single-deck blackjack. To see how this works, shuffle the deck and spread it faceup. To track the Ace of Spades, for example, notice the card just ahead of it. Suppose it is the King of Hearts (KH). You are going to shuffle and cut the deck and follow what happens to the pair of cards. Just to help you keep track, turn over the Ace of Spades and the card just ahead of it so they are faceup in the otherwise facedown deck. Now cut and shuffle once. One or more cards may get in between the Ace and the card that was just ahead, which we’re taking to be the King of Hearts, separating them. But if you were to play blackjack now with this deck, as soon as you saw the King of Hearts you would know that the Ace of Spades was likely to be close behind. As you successively cut and shuffle, still more cards crowd between the two cards. Sometimes, because the deck is cut for each shuffle, the order reverses and the Ace of Spades will appear first, in which case there is no prediction. If the deck is not shuffled well, the player can frequently tell that the corresponding Ace has a more-than-average chance of appearing soon. Applied to all four Aces, this is a powerful advantage.
Ace-locating led to the notion of following where groups of cards ended up after shuffling. Casinos typically use standardized shuffling techniques, which can be analyzed. Players, often with the aid of computers, learned to keep track of where chunks of cards rich in Aces and Tens were redistributed in the deck. The advantage gained from this could be substantial. The camouflage was effective as well since shuffle-trackers frequently found an advantage at the start of the first deal, betting big before having seen any cards. Other times, they raised their bets when the count was bad if they knew the next cards to be dealt had more than their share of Aces and Tens.
In 1997 Vivian and I went to St. George, Utah, where I ran in their annual marathon. On the way there and also coming back, we passed through Las Vegas. My friend Peter Griffin (no relation to the Griffin agency or its founders) of The Theory of Blackjack fame arranged with Joe Wilcox, who was then the casino manager at Treasure Island, to pay for (“comp”) our stay there. Joe agreed, if in return I would not play blackjack in any of Steve Wynn’s casinos. Joe was a gracious host and the room, food, and shows were excellent. He mentioned that the casinos were losing significant amounts to the shuffle-trackers and indicated that no one seemed to have found a shuffle that gave effective protection. After watching the dealers at Treasure Island and at two other casinos, and seeing what was wrong, with a little math I found a new shuffle that prevented tracking. I kept it to myself.
The players and the casinos fought not only at the tables and in the back rooms, but also in the courts. Nevada casinos were permitted to bar players, whereas New Jersey–ruled casinos could not. In both states, gaming establishments could always protect themselves by making the rules of the game more favorable to themselves or by reshuffling the cards at will. As to whether card counting was cheating, the statutes in Nevada clearly defined cheating as “to alter the selection of criteria which determine: (a) the result of a game; or (b) the amount or frequency of payment in a game”; using your brain to play well is clearly allowed. Introducing loaded dice would be cheating under clause (a), and adding or subtracting chips after you see your cards in blackjack would be cheating according to clause (b).
As the war between casinos and counters has evolved, so Las Vegas itself has been transformed. The early mob-dominated period was described in the bestselling 1964 book The Green Felt Jungle. Mob control gave way during the corporate transformation of the 1980s, the subsequent rise of the corporate gambling billionaires, and the ongoing expansion of gaming worldwide. Today the best players still thrive, but opportunities are increasingly limited and newcomers find success much more difficult.
The professional players share their stories each year at a private gathering in Nevada known as the Blackjack Ball. Hosted by professional card counter Max Rubin and sponsored by the Barona Casino, which is located hundreds of miles away in Southern California, many of the past and present best players in the world gather. Members of the Blackjack Hall of Fame are honored attendees. They also are featured in a picture gallery at the Barona, where they can stay for free but not play. The Barona benefits from the ball because any expert who attends must pledge never to play blackjack there—one of the most profitable investments ever by a casino.
My children, Raun, Karen, and Jeff, attended the ball with me in 2013, mixing with pseudonymous legends like James Grosjean, the Harvard mathematics graduate who has continued to develop and use new methods for “advantage play.” We spoke with the Holy Rollers, a card counting team of young Christians whose Robin Hood–like mandate is to transfer money from the casinos (“bad”) to their church (“good”) and themselves. Among the 102 guests, nearly half had net professional winnings of more than $1 million. The rest were family, spouses, and significant others. One of the champions was Blair Hull, who parlayed a fortune from running a blackjack team into several hundred million dollars at the Chicago Board Options Exchange. Bill Benter used his blackjack winnings to bankroll and build a billion-dollar worldwide business betting on horse races. A cheerful Taiwanese wearing the name tag B. J. TRAVELER sat down next to me with a shopping bag full of books he had written for the Chinese public about his adventures. He had played in sixty-four countries over six years, netting almost $7 million. Most amazing was that he survived a year in Moscow dodging thieves as he carted money from the casinos.
The next day, I had lunch on the strip with John Chang, a star of the MIT team featured in the movie 21, and an expert friend of his. Afterward, at a nearby casino, the three of us asked to have our picture taken in front of a blackjack table. Not allowed. So we sat down to play a hand or two at a $100-minimum/$10,000-maximum table with good rules. Chang and his friend whipped out rolls of $100 bills, peeled off $5,000 each, and bought in. “Our pockets are our banks,” they said. Our dealer, a friendly older woman from Eastern Europe, with no clue as to who was seated at her table, thought some of John’s unorthodox plays were beginner’s errors. When she advised him as to how to play correctly, he thanked her politely for her help and indicated a willingness to improve. Twenty minutes later, the casino was a few thousand dollars poorer and we had an employee take photos for us by the entrance.
Can an ordinary player still beat the game? My answer is a qualified yes. Many blackjack games have rules that have been changed enough so they are hard to beat. For instance, never play at a table where the payoff for getting a two-card 21, or blackjack, has been changed from the original 3:2 to lesser amounts like 6:5 or 1:1. There are newsletters and services that currently rate the games, and tell which ones are still good.
When I was the keynote speaker at the third World Game Protection Conference in Las Vegas in 2008, I was asked whether, when I wrote Beat the Dealer, I foresaw the magnitude and duration of its impact on the casino industry. I said that I didn’t know in 1962 if it would last five years or fifty, but now we know it has continued to this day.